Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 406 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 397 grams. Assume the population standard deviation is known to be 27. Is there sufficient evidence at the 0.02 level that the bags are underfilled?

Answer 1

Ho :   µ =   406                  
Ha :   µ <   406       (Left tail test)          
                          
Level of Significance ,    α =    0.02                  
population std dev ,    σ =    27.0000                  
Sample Size ,   n =    42                  
Sample Mean,    x̅ =   397.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   27.0000   / √    42   =   4.1662      
Z-test statistic= (x̅ - µ )/SE = (   397.000   -   406   ) /    4.1662   =   -2.16
                             
                          
p-Value   =   0.0154   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence to SAY THAT  bags are underfilled

..............

THANKS

revert back for doubt

please upvote